ACR CROSSES WRONG RWY WHEN CLRED TO CROSS.

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WE HAD JUST LANDED ON RWY 29R 25 MINS EARLIER AND HAD A QUICK TURN AROUND AT MSP. UPON PUSH BACK I COULD SEE ACFT LNDG ON 22. WE RECEIVED A TAXI CLRNC TO RWY 11L; HOLD SHORT OF RWY 22. I HAD A MIND SET THAT WE WERE CLRED TO RWY 22; HOLD SHORT OF RWY 11L. THE GND CTLR THEN QUESTIONED US ON OUR PRE-DEP CLRNC AND WE WERE INTERRUPTED ON OUR TAXI CHKS. THE HOLD SHORT POINT IS A COMMON INTXN GOING BOTH TO 11L AND 22 RWYS. WHEN CLRED TO CROSS I PROCEEDED TO THE APCH END OF RWY 22; RATHER THAN GOING AS INSTRUCTED TO 11L. TWR NOTED MY ERROR AFTER I HAD REACHED THE APCH END OF 22 AND REDIRECTED ME TO RWY 11L. 1) CONTRIBUTING FACTOR WAS THAT WE HAD BEEN UP UNTIL XA00 SLC TIME THAT SAME MORNING BECAUSE OF A RERTE. 2) WE HAD LANDED ON 29R 25 MINS EARLIER AND DID NOT EXPECT A TKOF INTO WHAT WAS LNDG TFC. 3) SEEING RWY 22 LNDG TFC; UPON PUSH BACK; AND SETTING IN MY MIND THAT THIS WAS THE DEP RWY. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATES TFC LNDG 22 WAS ONLY OTHER ACFT MOVING AT THE TIME OF INCIDENT. BELIEVES SEEING LNDG TFC HELPED CREATE HIS MIND SET AND ABILITY TO REVERSE THE RWY NUMBERS. ABILITY TO REVERSE THE RWY NUMBERS. THE QUERY REF PDC TOOK FO AND SO OUT OF THE LOOP AND SO NO ONE ELSE MONITORING TAXI. THE AREA WHERE HOLDING SHORT WAS COMMON TO TAXI ACROSS EITHER RWY. TWR DID NOT NOTICE UNTIL AT DEP END OF 22. TOO LATE!